Numerical Computation of Capacity for Discrete Memoryless Channels with Causal Side Information

The computation of capacity for discrete memoryless channels can be efficiently solved by using the Arimoto-Blahut (AB) iterative algorithm. However, the extension of this algorithm to compute the capacity for channels with Side Information (SI) is not straightforward, i.e. for channel with noncausal side information at the transmitter, because generally it is hard to evaluate the rates and capacities having auxiliary random variables. In this paper, we exploit an alternative reformulation of differential evolution optimization method to compute the capacity for channels with causal side information at the transmitter, and introduce an efficient algorithm to compute the capacity of these channels. Also, we extend the AB algorithm to compute the capacity of channels with side information at the receiver.